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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
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Spectral sequence of symmetric or exterior algebras?
This question is inspired by Hartshorne's exercise II.5.7 (c-d): the problem reads:
Let $0\rightarrow \mathcal{F}'\rightarrow\mathcal{F}\rightarrow\mathcal{F}''\rightarrow0$ be a short exact sequence …